Make decayEffect a continuous function of sample timestamp

Sources/LoopAlgorithm/LoopMath.swift

@@ -192,19 +192,25 @@ extension GlucoseValue {
         let glucoseUnit = LoopUnit.milligramsPerDeciliter
         let velocityUnit = GlucoseEffectVelocity.perSecondUnit
 
-        // The starting rate, which we will decay to 0 over the specified duration
-        let intercept = rate.doubleValue(for: velocityUnit) // mg/dL/s
-        let decayStartDate = startDate.addingTimeInterval(delta)
-        let slope = -intercept / (duration - delta)  // mg/dL/s/s
+        let firstChange = rate.doubleValue(for: velocityUnit) * delta // mg/dL/s * s = mg/dL
+        let secondChange = firstChange * (1 - delta / (duration - delta))
+
+        // Solve for f(t) = a*t^2 + b*t + c, where t is relative to self.startDate.
+        // f(0) = c
+        // f(delta) - c = firstChange = a*delta^2 + b*delta
+        // f(2*delta) - c = firstChange + secondChange = 4*a*delta^2 + 2*b*delta
+        // --> firstChange - secondChange = 2*a*delta^2
+        let c = quantity.doubleValue(for: glucoseUnit)
+        let a = (secondChange - firstChange) / (2 * delta * delta) // mg/dL/s^2
+        let b = (firstChange + secondChange - 4 * a * delta * delta) / (2 * delta) // mg/dL/s
 
         var values = [GlucoseEffect(startDate: startDate, quantity: quantity)]
-        var date = decayStartDate
-        var lastValue = quantity.doubleValue(for: glucoseUnit)
+        var date = startDate.addingTimeInterval(delta)
 
         repeat {
-            let value = lastValue + (intercept + slope * date.timeIntervalSince(decayStartDate)) * delta
+            let time = min(duration, date.timeIntervalSince(self.startDate))
+            let value = a * time * time + b * time + c
             values.append(GlucoseEffect(startDate: date, quantity: LoopQuantity(unit: glucoseUnit, doubleValue: value)))
-            lastValue = value
             date = date.addingTimeInterval(delta)
         } while date < endDate
 

Tests/LoopAlgorithmTests/Fixtures/carbs_with_isf_change_recommendation.json

@@ -1,5 +1,5 @@
 {
   "manual" : {
-    "amount" : 10.546890782709953
+    "amount" : 10.52269112701204
   }
-}
+}